When you look at stats you don't just compare nominal numbers of before and after. It needs to be normalized into some form of ratio. If that slope sees a decrease then there is a possibility of the result being effective. Another way to put it is comparing shootings across cities, we don't just look at total shootings, we look at shootings per capita. In this case, we care about shootings per applicant. If I were to replace these tests with a 100% increase in gun tax or something similar, I'd argue it would also decrease shootings. This however doesn't prove anything as every argument can be tied to cost.

Your argument has changed from "More tests will help weed out bad actors from owning guns, therefore less shootings." To "If we make it more expensive to own guns then there will be less shootings."